A wire has a mass `(0.3+-0.003)g`, radius `(0.5+-0.005)mm` and length `(6+-0.06)cm`. The maximum percentage error in the measurement of its density is -

Options

A. 1
B. 2
C. 3
D. 4

Answer

D

Explanation

`rho = (M)/(V) = (M)/(pir^(2)l)`
`(Delta rho)/(rho) = (Delta M)/(M) + ( 2Delta r)/(r ) + (Delta l)/(l) ` (For maximum error)
`(Delta M)/(M) xx 100 = (0.003)/(0.3) xx 100 = 1%`,
`(Deltar)/(r ) xx 100 = (.005)/(0.5) xx 100 = 1%`
`(Delta l)/(l) xx 100 = (0.06)/(6) xx 100 = 1%`
`rArr (Delta rho)/(rho) xx 100 = 4%`